Abstract
Nous présentons le système tridimensionnel d’équations d’Eringen pour la nématodynamique des cristaux liquides, annonçons l’existence en temps et l’unicité de solutions fortes pour le problème unidimensionnel dans le cas périodique et montrons la dépendance continue de la solution sur les données initiales.
Highlights
In papers [1,2,3,4] and [5], we considered the Ericksen–Leslie system of equations for nematodynamics and proved the existence and uniqueness theorems
The Ericksen–Leslie equations do not take into account micromomentum of molecules
We write down the right Eringen system of equations, which takes into account the micromomentum of molecules, and study the same question of unique solvability
Summary
In papers [1,2,3,4] and [5], we considered the Ericksen–Leslie system of equations for nematodynamics and proved the existence and uniqueness theorems. The Ericksen–Leslie equations do not take into account micromomentum of molecules. We write down the right Eringen system of equations (see [6] and [7]), which takes into account the micromomentum of molecules, and study the same question of unique solvability. We consider the simplest form of Eringen’s system for the nematodynamics of liquid crystals (see Figure 1 for example) and prove the local solvability of the corresponding initial–boundary value problem. The existence of global solutions of the general Eringen system is still an open question. It is natural to expect local solvability and for the weak solutions, global solvability
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